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Consider, as nodes for polynomial interpolation, the  n th roots of unity. For a sufficiently smooth function      f ( z ) f(z)      , we require a polynomial      p ( z ) p(z)       to interpolate  f  and certain of its derivatives at each node. It is shown that the so-called Pólya conditions, which are necessary for unique interpolation, are in this setting also sufficient.

Hermite-Birkhoff interpolation in the 𝑛th roots of unity